Question

for problems 1–7, define the variable, write and solve an equation to represent the situation, and check your solution. 1. the local zoo has 900 pounds of bamboo to feed a giant panda. on average, a giant panda eats 30 pounds of bamboo each day. the panda has eaten 390 of the 900 pounds of bamboo. how many more days can the panda eat before the zoo must buy more bamboo? 2. the track team is having a fundraiser. jonas sets a personal goal of raising a total of $225. so far he has raised $162 without running any laps. for each lap he runs, he will raise an additional $3. how many laps must jonas run to meet his goal?

Explanation:

Problem 1

Step1: Define variable

Let \( d \) be the number of days the panda can eat more.

Step2: Find remaining bamboo

Remaining bamboo: \( 900 - 390 = 510 \) pounds.

Step3: Write equation

The panda eats 30 pounds per day, so \( 30d = 510 \).

Step4: Solve for \( d \)

Divide both sides by 30: \( d=\frac{510}{30}=17 \).

Step5: Check solution

Total bamboo eaten: \( 390 + 30\times17 = 390 + 510 = 900 \), which matches the total bamboo.

Step1: Define variable

Let \( l \) be the number of laps Jonas must run.

Step2: Write equation

Money from laps: \( 3l \), total raised: \( 162 + 3l = 225 \).

Step3: Solve for \( l \)

Subtract 162: \( 3l = 225 - 162 = 63 \), divide by 3: \( l = \frac{63}{3}=21 \).

Step4: Check solution

Total raised: \( 162 + 3\times21 = 162 + 63 = 225 \), which matches the goal.

Answer:

The panda can eat for 17 more days.

Problem 2